Tung H. Nguyen

Email: tunghn [at] math.princeton.edu
Office: 218 Fine Hall, Washington Road, Princeton, NJ 08544

Hello! I am Tung Nguyen, a final year PhD student in PACM and a Jacobus Fellow at Princeton University, working with Paul Seymour. Before Princeton, I earned a Bachelor of Science (with Honors) in Mathematical Sciences from KAIST, where my thesis advisor was Sang-il Oum.

My Vietnamese name is Nguyễn Huy Tùng.

I am interested in discrete mathematics, mostly structural and extremal problems in graph theory.

I have maintained the lists of problems submitted to two Barbados graph theory workshops: 2022a and 2024.

Some notes on recent work on the Erdős–Hajnal conjecture.

Papers

Preprints

  1. Off-diagonal Erdős–Hajnal for $P_5$, manuscript.
  2. On polynomially high-chromatic pure pairs, manuscript.
  3. Coarse tree-width (with A. Scott and P. Seymour), preprint.
  4. Distant digraph domination (with A. Scott and P. Seymour), preprint.
  5. Trees and near-linear stable sets (with A. Scott and P. Seymour), preprint.
  6. Induced subgraph density. VII. The five-vertex path (with A. Scott and P. Seymour), preprint.
  7. Induced subgraph density. VI. Bounded VC-dimension (with A. Scott and P. Seymour), preprint. [Talks by Alex and by me]
  8. Induced subgraph density. V. All paths approach Erdős–Hajnal (with A. Scott and P. Seymour), preprint.
  9. Induced subgraph density. IV. New graphs with the Erdős–Hajnal property (with A. Scott and P. Seymour), preprint. [A talk by me]
  10. Induced subgraph density. III. Cycles and subdivisions (with A. Scott and P. Seymour), preprint.
  11. Linear-sized minors with given edge density, preprint.

Accepted/Published

  1. Subdivisions and near-linear stable sets (with A. Scott and P. Seymour), Combinatorica, accepted.
  2. Graphs without a 3-connected subgraph are 4-colourable (with E. Bonnet, C. Feghali, A. Scott, P. Seymour, S. Thomassé, and N. Trotignon), Electron. J. Combin. 32 (2025), no. 1, Paper No. 1.26, 11pp.
  3. Some results and problems on tournament structure (with A. Scott and P. Seymour), J. Combin. Theory Ser. B 173 (2025), 146–183.
  4. A counterexample to the coarse Menger conjecture (with A. Scott and P. Seymour), J. Combin. Theory Ser. B 173 (2025), 68–82.
  5. Induced subgraph density. II. Sparse and dense sets in cographs (with J. Fox, A. Scott, and P. Seymour), European J. Combin. 124 (2025), Paper No. 104075.
  6. Polynomial bounds for chromatic number. VIII. Excluding a path and a complete multipartite graph (with A. Scott and P. Seymour), J. Graph Theory 107 (2024), 509–521.
  7. Induced subgraph density. I. A $\text{loglog}$ step towards Erdős–Hajnal (with M. Bucić, A. Scott, and P. Seymour), Int. Math. Res. Not. IMRN 12 (2024), 9991–10004. [Talks by Paul and by me]
  8. A note on the Gyárfás–Sumner conjecture (with A. Scott and P. Seymour), Graphs Combin. 40 (2024), no. 2, Paper No. 33, 6pp.
  9. Highly connected subgraphs with large chromatic number, SIAM J. Discrete Math. 38 (2024), no. 1, 243–260.
  10. Clique covers of $H$-free graphs (with A. Scott, P. Seymour, and S. Thomassé), European J. Combin. 118 (2024), Paper No. 103909, 10 pp.
  11. On a problem of El-Zahar and Erdős (with A. Scott and P. Seymour), J. Combin. Theory Ser. B 165 (2024), 211–222. [A talk by Alex]
  12. Induced paths in graphs without anticomplete cycles (with A. Scott and P. Seymour), J. Combin. Theory Ser. B 164 (2024), 321–339.
  13. A further extension of Rödl's theorem, Electron. J. Combin. 30 (2023), no. 3, Paper No. 3.22, 16pp.
  14. Growing balanced covering sets, Discrete Math. 344 (2021), no. 11, Paper No. 112554, 6pp.
  15. The average cut-rank of graphs (with S. Oum), European J. Combin. 90 (2020), Paper No. 103183, 22 pp.

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